title: Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures.
abstract: We introduce a construction to "periodize" a quasiperiodic lattice of obstacles, i.e., embed it into a unit cell in a higher-dimensional space, reversing the projection method used to form quasilattices. This gives an algorithm for simulating dynamics, as well as a natural notion of uniform distribution, in quasiperiodic structures. It also shows the generic existence of channels, where particles travel without colliding, up to a critical obstacle radius, which we calculate for a Penrose tiling. As an application, we find superdiffusion in the presence of channels, and a subdiffusive regime when obstacles overlap.
authors.affiliation: Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510, Mexico.
authors.forename: Atahualpa S
authors.initials: AS
authors.lastname: Kraemer
authors.forename: David P
authors.initials: DP
authors.lastname: Sanders